I am dual booting Ubuntu 12.04 on a Lenovo G770. The internal mic works fine in Windows 7. The mic is recognized and unmuted, but it just isn't detecting any sound. I tried messing around with pavucontrol settings, but to no avail.
I also have a G770, and I (finally) got my internal microphone working yesterday by following directions posted here.
Here's what I did:
Opened "/etc/modprobe.d/sound.conf" with sudo rights (in my case this file did not exist, so I simply created it)
Added the following line to "sound.conf": "options snd-hda-intel model=asus"
Saved "sound.conf" and rebooted
BOOM, working microphone!